An Adaptive Euler--Maruyama Scheme for Stochastic Differential Equations with Discontinuous Drift and its Convergence Analysis

DOI10.1137/18M1170017zbMATH Open1418.60062arXiv1802.04521WikidataQ128388536 ScholiaQ128388536MaRDI QIDQ4624977

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Publication date: 20 February 2019

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Abstract: We study the strong approximation of stochastic differential equations with discontinuous drift coefficients and (possibly) degenerate diffusion coefficients. To account for the discontinuity of the drift coefficient we construct an adaptive step sizing strategy for the explicit Euler-Maruyama scheme. As a result, we obtain a numerical method which has -- up to logarithmic terms -- strong convergence order $1/2$ with respect to the average computational cost. We support our theoretical findings with several numerical examples.

Full work available at URL: https://arxiv.org/abs/1802.04521

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